A young girl has become the third person to die in the UK after catching swine flu, as the total of confirmed cases in the country passed 6,000.

The girl, who had other significant health problems, died at Birmingham children's hospital on Friday evening. Her death is the first in England associated with swine flu, although it is not yet known if it contributed to her death.

Two people, also with other significant health problems, died at a hospital in Paisley, Scotland. They were an unnamed 73-year-who died on Saturday night after 15 days in intensive care, and Jacqui Fleming, 38, who died after giving birth prematurely more than two weeks ago.

As details of the girl's death emerged, the government's Health Protection Agency announced a big jump of 1,604 in the number of patients in England confirmed with swine flu. The figure for the UK as a whole rose to 6,133. Changes in the way health officials are confirming cases in areas where the disease is most prevalent may complicate judgments about how fast the disease is spreading.

The chief medical officer, Sir Liam Donaldson, has already warned that there may be tens of thousands of cases each week this autumn, because the virus is more likely to thrive in a colder climate.

The family of the girl who died has asked for her identity to be kept private. Andy Burnham, the health secretary, said: "Tragic as today's death is, I would like to emphasise that, across England, the majority of swine flu cases have not been severe.

"The risk to the public remains low and we can all play our part in slowing the spread of the virus by following simple hygiene procedures – like washing your hands and using tissues when coughing or sneezing. We are making sure arrangements are in place so that the UK remains well placed to deal with this pandemic."

Vivienne Nathanson, head of science and ethics at the British Medical Association, said: "Flu can kill completely healthy people if they get pneumonia, but if they have got health problems they are more likely to get complications.

Nathanson said that as public health officials gathered more information on complications, doctors might start to be able to identify higher risk groups at higher risk. "That will help us in future to vaccinate the people at highest risk."

Six people had suspected swine flu at the Glastonbury festival. Health officials said this was remarkably low, but the incubation period of three to four days means other cases may emerge.

A handful of ball boys and girls at Wimbledon, where attendance has reached 40,000 a day, have been advised to stay at home after suffering flu-like symptoms. Anyone with symptoms has been advised to ring NHS Direct or GP surgeries for advice, rather than going to surgeries and risking infecting more people.

Because of the outbreak's scale, health officials in hotspots such as London, the West Midlands and parts of Scotland are no longer tracing people who have come into contact with confirmed cases. Doctors are now confirming cases on the spot, rather than through laboratory results. The official statistics at present include only cases confirmed in laboratories.

The jump reported in England covered new cases confirmed between Thursday lunchtime and Sunday lunchtime. But the figure for Scotland rose later in the day from 922 to more than 1,118, six of whom were being treated in hospital.

Scientists have found the first case of the new H1N1 influenza strain showing resistance to Tamiflu, the main antiviral flu drug, Danish officials and the manufacturer said yesterday. It was expected that the strain would at some point show resistance to Tamiflu, Denmark's State Serum Institute said. The patient was now well and no further infection with the resistant virus had been detected.